Four numbers are chosen at random (without replacement) from the set 1,2,3, ., 20 . Statement-1: The probability that the chosen numbers when arranged in some order will form an AP is 1 85 . Statement-2: If the four chosen numbers from an AP, then the set of all possible values of common difference is 1, 2, 3, 4, 5 .

Step-by-step solution

N ( S )= ²⁰ C ₄ Statement-1: common difference is 1 ; total number of cases =17 common difference is 2 ; total number of cases =14 common difference is 3 ; total number of cases =11 common difference is 4 ; total number of cases =8 common difference is 5 ; total number of cases =5 common difference is 6 ; total number of cases =2 Prob. = 17+14+11+8+5+2 ²⁰ C ₄ = 1 85 .